The interdependence of tropospheric CH4, CO and OH is explored using a simple analytic three‐component box model. The steady state solution for this model places constraints on the relative strengths of the source fluxes of CH4and CO and the production rate for OH. It is demonstrated that if these quantities vary independently the system can only remain stable for a narrow range of conditions. In order for the system to remain stable and well‐behaved for a wide range of fluxes, the fluxes of CO and CH4and the production rate for OH must be covariant, either due to internal feedback processes or to coordinated response to external conditions. The observed steady state abundances of methane in ice records representing preindustrial and glacial times, although sparse, suggest covariant fluxes and OH production. Otherwise the global flux of methane must have varied by less than about 20 during deglaciation and emergence of the boreal wetlands, a period of major change in global hydrology, climate, and biome distributi
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